Objects for MWR

Computers and Chemical Engineering

Volumn 26, Issue 7-8, 2002, Pages 981-998

  Adomaitis, Raymond A ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

Distributed parameter systems; Galerkin's method; Object oriented programming; Spectral methods; Weighted residual methods

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFUSION; FLOW OF FLUIDS; GALERKIN METHODS; NUMERICAL METHODS;

COMPUTATIONAL FRAMEWORKS;

CHEMICAL ENGINEERING;

COMPUTER ANALYSIS;

ARTICLE; CATALYST; CHEMICAL ENGINEERING; FLOW RATE; GAS; GEOMETRY; HEAT TRANSFER; MATHEMATICAL ANALYSIS; MATHEMATICAL PARAMETERS; TEMPERATURE; VELOCITY; WEIGHTED RESIDUAL METHOD;

EID: 0037104856     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0098-1354(02)00040-6     Document Type: Article

References (29)

1. Adomaitis, R. A. (2001). Spectral filtering for improved performance of collocation discretization methods. Computers and Chemical Engineering, 25, 1621-1632.
2. Adomaitis, R. A., & Lin, Y.-H. (1998). A technique for accurate collocation residual calculations. Chemical Engineering Journal, 71, 127-134.
3. Ascher, U., Christiansen, J., & Russell, R. D. (1981). Collocation software for boundary-value ODEs. ACM Transactions on Mathematical Software, 7, 209-222.
4. Ascher, U., Mattheij, R. M., & Russell, R. D. (1988). Numerical solution of boundary value problems for ordinary differential equations. Englewood Cliffs, NJ: Prentice Hall.
5. Burggraf, O. R. (1966). Analytical and numerical studies of the structure of steady separated flows. Journal of Fluid Mechanics, 24, 113-151.
6. Chang, H.-Y., & Adomaitis, R. A. (1999). Analysis of heat transfer in a chemical vapor deposition reactor: An eigenfunction expansion solution approach. International Journal of Heat and Fluid Flow, 20, 74-83.
7. Chang, H.-Y., Adomaitis, R. A., Kidder, J. N., & Rubloff, G. W. (2001). Influence of gas composition on wafer temperature in a tungsten chemical vapor deposition reactor: experimental measurements, model development, and parameter estimation. Journal of Vacuum Science and Technology, B, 19, 230-238.
8. Choo, J. & Adomaitis, R. A. (2002) Assessment of computational methods for implementing weighted residual methods based on very high degree polynomial approximations, manuscript in preparation.
9. Cooper, J. M. (1998). Introduction to partial differential equations with MATLAB. Boston, MA: Birkhauser.
10. Don, W. S. & Solomonoff, A. (1997) PseudoPack-Pseudo-Spectral Differentiation Software Package User Manual for version 2.3 beta Brown University, Providence, RI.
11. Fokkema, D. R., Sleijpen, G. L. G., & Van der Vorst, H. A. (1998). Accelerated inexact Newton schemes for large systems of nonlinear equations. SIAM Journal of Scientific Computing, 19, 657-674.
12. Gottlieb, D., & Shu, C.-W. (1997). On the Gibbs phenomenon and its resolution. SIAM Review, 39, 644-668.
13. Joseph, D. D., & Sturges, L. (1978). The convergence of biorthogonal series for biharmonic and Stokes flow edge problems: part II. SIAM Journal of Applied Mathematics, 34, 7-26.
14. Langtangen, H. P., & Munthe, O. (2001). Solving systems of partial differential equations using object-oriented programming techniques with coupled heat and fluid flow as example. ACM Transactions on Mathematical Software, 27, 1-26.
15. Langtangen, H. P. (1999) Computational Partial Differential Equations: Numerical Methods and Diffpack Programming, Lecture Notes in Computational Science and Engineering, Vol. 2, Springer-Verlag.
16. Lew, H. S., & Fung, Y. C. (1969). The motion of the plasma between the red blood cells in bolus flow. Biorheology, 6, 109-119.
17. Lin, Y.-h., & Adomaitis, R. A. (2001). Simulation and model reduction methods for an RF plasma glow discharge. Journal of Computational Physics, 171, 731-752.
18. Lin, Y.-H., Chang, H.-Y., & Adomaitis, R. A. (1999). MWRtools: a library for weighted residual methods. Computers and Chemical Engineering, 23, 1041-1061.
19. Madsen, N. K., & Sincovec, R. F. (1979). Algorithm 540: PDECOL, general collocation software for partial differential equations. ACM Transactions on Mathematical Software, 5, 326-351.
20. Pan, F., & Acrivos, A. (1967). Steady flows in rectangular cavities. Journal of Fluid Mechanics, 28, 643-655.
21. Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. (1988). Numerical recipes in C. New York: Cambridge University Press.
22. Rice, R. G., & Do, D. D. (1995). Applied mathematics and modeling for chemical engineers. New York: Wiley.
23. Shampine, L. F., Kierzenka, J. & Reichelt, M. W. (2000) 'Solving boundary value problems for ordinary differential equations in Matlab with bvp4c,' preprint.
24. Shankar, P. N. (1993). The eddy structure in Stokes flow in a cavity. Journal of Fluid Mechanics, 250, 371-383.
25. Srinivasan, R. (1995). Accurate solutions for steady plane flow in the driven cavity. I. Stokes flow. ZAMP, 46, 524-545.
26. Trefethen, L. (2000). Spectral methods in MATLAB. SIAM.
27. Villadsen, J. V., & Stewart, W. E. (1967). Solution of boundary-value problems by orthogonal collocation. Chemical Engineering Science, 22, 1483-1501.
28. Villadsen, J. & Michelsen, M. L. (1978) Solution of Differential Equation Models by Polynomial Approximation, Int. Series in Phys. and Chem. Engng. Sci., Prentice-Hall, Englewood Cliffs, NJ.
29. Weideman, J. A. C., & Reddy, S. C. (2000). A MATLAB differentiation matrix suite. ACM Transactions on Mathematical Software, 26, 465-519.